Can you do a visit to see it before the first time you use it? Might make you feel a bit better? Maybe even with your DC? Arrange to get to the school gates a few minutes before end of day, watch what happens and how they round the kids up and walk them there, see what happens?
If that's not possible, can you call the person who runs it, explain you are nervous as it's the first time you've used outside school care, and ask the questions you are worried about. Eg how do they make sure they collect all the kids, what would DV do if she missed the collection sometime, what activities do they do at club, could she sit quietly and read or do homework if she wants to, etc? Is there anyone else in DC's class who goes regularly who could show her the ropes on day 1?
As someone who has used after school care and holiday clubs since DS1 was 4 years old, I can tell you it will almost certainly run like a well-oiled machine and be absolutely fine. But rather than sitting fretting, have the conversation with the staff and you'll feel much better.
Also talk to DV about what she would do if she didn't get picked up (which is basically tell one of the teachers at school "I was supposed to be collected for after school club and they didn't take me, can you please help me").